Well, sometimes that's how it goes Daddy-O.
To be serious, a bad battery has a short and it will kill your alternator because it's full chat trying to charge up this dead battery everytime the motor starts. Same goes for the starter. Lower voltage creates a high amperage draw and associated heat. The longer one of the brushes stays on one commutater bar (the copper bars on the end of the starter armature), the more heat is generated.
If one of my starters "grunts" one time, I'm checking the alternator and battery cables that day and if the they are good, the battery just gets replaced.